Grünwald and van Ommen's claim is that, for a sufficiently small learning rate \(\eta \) , certain model misspecification biases can be repaired. Of course, the threshold defining “sufficiently small” cannot be known in practice, so some data-driven choices are required. [1]}, [2]}, [3]}, and [4]} developed a so-called SafeBayes algorithm to choose the learning rate \(\eta \) , based on minimizing a sequential risk measure. A number of other learning rate selection methods have been proposed recently, including the two distinct information matching strategies in [5]} and [6]}, and bootstrap-motivated calibration methods of [7]}.
Since the role played by the learning rate is relatively unfamiliar and since the various methods differ significantly in terms of their motivations and implementations, it would be beneficial to see a head-to-head comparison in terms of some standard metrics, for example, the validity and efficiency of the corresponding generalized Bayes credible regions. This paper aims to fill this gap.
